I can't seem to figure out the logic behind this problem.
Would this problem have something to do with mode?
I know I am missing the main point of this problem.
Since is an odd number it must be perfect square also . So:
Now, if we make substitution we can write :
This equality has integer solutions only if is power of so must be an odd number so we shall make substitution and therefore :
It is obvious that both and must be powers of and this is possible only if , therefore :